1. Field of the Invention
The present invention relates to methods for measuring stress within an object. More specifically, the invention relates to a method for determining residual stress within materials.
2. Relevant Technology
The composition of natural and man made materials is well understood. We know that materials are made up of atoms that are bonded by atomic forces to form solids. Atoms may also combine with other atoms to form molecules. These molecules may be bonded closely together, as with solids, or far apart, as with gases. The state of the material, solid, liquid, or gas, depends on the amount of energy the molecules have. Because molecules and atoms have no known structural connection, they are free to move and act in response to the attraction forces of the molecules and atoms around them. These attraction forces may be conceptualized as very small springs which connect each atom, and/or molecule. The strength or weakness of the attraction forces depends largely on the amount of energy the atom is exposed to. Because the molecules and atoms of an object are exposed to different amounts of energy atoms at one location within an object may be pulled or pushed by other atoms.
These push and pull forces are known as stress. Stress is a force divided by an area. The force is the atomic attraction force and the area is a measured area of an object. In common elements such as iron or copper, the atoms are atomically bond together in a very tight lattice. Because different atoms of an object are exposed to varying amounts of energy, the stress of one or more atoms on neighboring atoms varies throughout the material. The different magnitudes of stress throughout an object are known as residual stress.
The name comes primarily from the fact that residual stress is the stress remaining within an object as a result of forming, shaping or otherwise processing the object. Generally, objects are formed by exposure to a change in energy, or heat, and an application of pressure. For example, diamonds are carbon atoms which have undergone extreme heat and pressure. The heat and pressure apply stress to the diamond. When the heat and pressure are removed, the atoms making up the diamond react by pulling and pushing each other. The push and pull within the diamond is residual stress, the stress left after application of the formation stress.
Similarly, man made objects experience some form of processing before the final product or object is ready for use. Particularly with metals, there are a number of processing methods which may be used to form, shape and refine the elements into metallic objects made of one element or composite objects made of two or more elements. For example, steel is made from combining iron and carbon. Other steel alloys are made using iron, carbon, and other natural or man made elements. Processing methods for creating steel or other metallic alloys include, forging, case hardening, quenching, welding, bonding, casting, extruding, and the like. These methods involve heating the elements and applying pressure to shape the object. From steel other objects may be created. These objects may require that the steel be rolled, hammered, stamped, drilled, machined, or otherwise shaped.
Whenever an object is exposed to a change in temperature, or application of pressure, the atoms within the object react by increasing or decreasing their attraction on neighboring atoms. This changes the residual stress within the object. Residual stress may not be a major concern in large applications of an object, such as the blade of a shovel. But, residual stresses contributes to failures from fatigue, fracture, distortion, wear, creep, stress corrosion cracking and the like. Material may also be processed to make parts of machines where a variation in size or performance of a part may cause serious problems.
For example, military fighter planes are generally made of metal and metal alloy parts. Due to the stress and change in temperature operation of the fighter places on the parts, the parts are precision machined and engineered to exact specifications. The problem is the residual stresses within a part may cause the part to distort, or deform during use, or prior to installation such that the part is unusable. This may be very costly. One estimate suggests that the cost of distorted scrapped fighter plane parts is around $263 million.
Techniques do exist for calculating the residual stress within an object. In the hole drilling method, a strain gauge rosette is placed on a free surface of the object. Then, a hole is drilled in the middle of the rosette. The strain gauge rosette is then used to measure the strain of the surface once the hole is cut. In the layer removal method, changes in one existing surface are measured after a layer of material is removed from an opposite surface. In the compliance method, the strain is measured near or opposite a successively extended slot. Other techniques such as Moire interferometry also exist.
These techniques as well as the method of the present invention, relate to elastic materials. Elastic materials are those which deform in response to internal or external stresses placed on the object. All materials are elastic to some degree. These techniques measure the residual stress by calculating how much the material deformed after some of the material is removed through removing a layer, drilling a hole, and the like. The material deforms once a hole or other material is removed because the residual stress within the material is freed through creation of the hole, cut, or layer.
These techniques are related because each performs the measurements on a pre-existing surface of the object. The problem is that measuring a change in a pre-existing surface is not as precise as measuring the new free surface created by cut, hole, or layer removal. Because stress is not being released at the pre-existing surface, any changes in the pre-existing surface are approximations of the deformation at the newly created surface which caused the measured deformation at the pre-existing surface. In other words, the accuracy of measurements taken at a pre-existing surface is limited due to the remoteness between where the residual stress is relieved and where the measurements are made.
Additionally, because the measurements are indirect representations of the displacement at the newly formed surface, the calculations to arrive at the residual stress at the newly created surface are complex. The calculations involve theoretically complex and tedious inversion calculations simply to determine the residual stress in a single dimension. Completing the calculations and reducing the measurements to the residual stresses may take several weeks, particularly if an analyst needs to know the residual stress in two or three dimensions.
Measuring the new free surface would allow one to calculate the residual stress which existed prior to removal of the material. However, there is not a reference point which may be used to determine the amount of change in the new free surface after the material is removed. In addition, other techniques may avoid measuring deformation at the new free surface because the drill bit, or cutting tool introduced residual stress into the material during the removal process.
Therefore, it would be an advancement in the art to provide a system and method for determining the residual stress within an elastic object at a new free surface where the residual stress is being relieved. It would be a further advancement to provide a system and method for determining the residual stress within an elastic object such that the calculations are simple and direct rather than inversion calculations involving complex theory. It would be another advancement in the art to provide a system and method for determining the residual stress within an elastic object such that an analyst does not need special training or expertise to perform the measurements.
The invention is a system and method for determining the residual stress within an elastic object. The method includes measurements of a real world object as well a computer model of the object.
First, an elastic object is cut through a path. Preferably, the path is a plane having a known location and perpendicular orientation with respect to the object. The cut is preferably made using a tool which introduces minimal residual stress into the object. The cut creates a new free surface on either side of the cut. Due to the elasticity of the object and the residual stress, the free surface deforms once the cut is made.
Next, one of the two free surfaces is measured to identify a contour of the new free surface. The contour measures the deformation of the free surface from the path. This deformation or displacement represents the amount of relief in the free surface caused by the residual stress after the cut is made. The contour is defined by points measured in a direction parallel to the path. These points represent areas of deformation on the free surface. The contour may be measured in one, two, or three dimensions The measurements are recorded in an empirical data set.
Then, a model of a portion of the object which includes the free surface is created in a computer simulator. The computer simulator may employ the finite element method (FEM). These computer simulators may also be known as FEM simulators. Using the FEM simulator, a model of the portion of the object is created to represent the portion of the real object which includes the measured free surface.
The model of the portion may be defined by a finite set of elements which interconnect to define the portion. The portion as a whole and each of the elements of the portion act in relation to boundary conditions. A boundary condition is a type of force or constraint which may be applied to the portion. A plurality of boundary conditions may act on a portion at any given time.
Boundary conditions are generally defined for the whole exposed surface of the portion. The FEM simulator then applies the boundary conditions to each element individually. Boundary conditions may be of various types including a force, a moment, a distributed load and the like. For each of these types of boundary conditions different properties of the portion may be defined. For example a moment boundary condition may require that the force and the moment arm be defined. A force boundary condition may require a value for the force and an indication of where on the portion the force acts.
Generally, a set of initial conditions are defined for an object at the time the object is created. An FEM simulator allows initial conditions to be defined for known residual stress within an object. In a preferred embodiment, no initial conditions are defined to model residual stress. Alternatively, the present invention may be practiced with initial conditions which define residual stress.
The steps of defining the equilibrium equations and applying these equations to each element may be referred to as initialization. Initialization includes defining properties for individual elements in the model. These properties may include the modulus of the material, the poisson ratio, and the kind of material which makes up the portion.
If an elastic material is cut, material is removed, then the new free surface deforms due to the residual stresses. Under Bueckner""s superposition principle, if the free surface is returned to its position prior to deformation, the difference between the original position and the new deformed position may be used to determine the residual stress at that point prior to the cut. The residual stress caused the point to change position. Using the empirical data set and the FEM simulator, the superposition principle is applied.
The empirical data is entered into the FEM simulator. The empirical data represents the position of points along the free surface in a x, y, and z axis coordinate system related to the real object. The empirical data is entered as a displacement boundary constraint having a different sign than that originally measured in relation to the path. The model portion has corresponding points along the free surface of the model.
Then, the FEM simulator calculates the residual stress by reviewing each element along the displacement boundary constraint to points along the path. The change in position and the properties of the elements of the portion are used by the FEM to calculate residual stress along the path. Using the path as a point of origin, the difference in sign indicates which direction the stress acts perpendicular to the path. The residual stress along the path is accumulated into residual stress data which may be directly examined, presented in a color coded stress map, or otherwise utilized by an analyst interested in the residual stress of the object.
One embodiment of the present invention may comprise the aforementioned method steps. It is understood that variations in the steps of the method or components of the system may be made and still come within the scope of the present invention. These and other features and advantages of the present invention will become more fully apparent from the following description and appended claims, or may be learned by the practice of the invention as set forth hereinafter.